Finite Group Databasebeta

← #21450136

Subgroups — #21450136

Order 7808.

584 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊Dic61C211yesmaximal, characteristic, complemented
2#16839701C212yesmaximal, complemented
3#16839698C212yesmaximal, complemented
4#16839660C212yesmaximal, complemented
5#16839642C212yesmaximal
6#16839634C212yesmaximal, complemented
7#16839622C212yesmaximal, complemented
8#16839622C211yesmaximal, characteristic, complemented
9C2×C4×D4×C61C211yesmaximal, characteristic
10C23×Dic61C2212yes—
11C2×C4⋊Dic61—24no—
12C2×C4⋊Dic61C2212yes—
13C2×C4⋊Dic61C2212yes—
14C2×C4⋊Dic61C2212yes—
15C2×#11758196C2214yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2214yes—
18#14519684C2212yes—
19#14519684C2214yes—
20#14519684C2214yes—
21C22×D4×C61C2211yescharacteristic
22C23×C4×C61C2211yescharacteristic
23C23×C4×C61C2211yescharacteristic
24C4×D4×C61—24no—
25C2×C4⋊C4×C61C2211yescharacteristic
26C2×C22⋊C4×C61C2211yescharacteristic
27C2×C22⋊C4×C61C2211yescharacteristic
28C2×C42×C61C2211yescharacteristic
29C24×C61C2311yescharacteristic
30C24×C61C2311yescharacteristic
31C2×D4×C61—22no—
32C2×D4×C61—22no—
33C2×D4×C61Q814yes—
34C22×C4×C61—24no—
35C22×C4×C61—22no—
36C22×C4×C61—24no—
37C22×C4×C61D414yes—
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×Dic61—24no—
44C22×Dic61—44no—
45C22×Dic61C2314yes—
46C22×Dic61C2314yes—
47C4⋊C4×C61—22no—
48C22⋊C4×C61—22no—
49C22⋊C4×C61—22no—
50C42×C61—22no—
51C22⋊Dic61—24no—
52C22⋊Dic61—44no—
53C4⋊Dic61—24no—
54C4⋊Dic61—24no—
55C4⋊Dic61—24no—
56#11758196—44no—
57C23×C61—22no—
58C23×C61—22no—
59C23×C61—21no—
60C23×C61—22no—
61C23×C61—21no—
62C23×C61—22no—
63C23×C61C2×D412yes—
64C23×C61C2×Q812yes—
65C23×C61C2×Q812yes—
66C23×C61#4112yes—
67C23×C61C2411yescharacteristic
68D4×C61—28no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61—21no—
72C2×C4×C61—28no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—44no—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2×Q812yes—
81C2×C4×C61#4114yes—
82C2×Dic61—24no—
83C2×Dic61—24no—
84C2×Dic61—24no—
85C2×Dic61—24no—
86C2×Dic61—24no—
87C2×Dic61—24no—
88C2×Dic61—48no—
89C22×C61—22no—
90C22×C61—22no—
91C22×C61—24no—
92C22×C61—24no—
93C22×C61—22no—
94C22×C61—24no—
95C22×C61—41no—
96C22×C61—41no—
97C22×C61—42no—
98C22×C61C22⋊Q814yes—
99C22×C61C22×D411yescharacteristic
100C22×C61C22×Q811yescharacteristic
101C22×C61C2×#4112yes—
102C22×C61C2×#4111yescharacteristic
103C22×C61H(5,𝔽2)12yes—
104C4×C61—22no—
105C4×C61—22no—
106C4×C61—41no—
107C4×C61—41no—
108C4×C61#12314yes—
109Dic61—44no—
110Dic61—44no—
111#2487—611nomaximal, Sylow
112C2×C61—24no—
113C2×C61—42no—
114C2×C61C2×C22⋊Q811yescharacteristic
115C2×C61C2×#12311yescharacteristic
116C2×C61#53511yescharacteristic
117C2×C61#55312yes—
118C2×C61#55412yes—
119C2×C4×D4D6111yescharacteristic
120C22×C4⋊C4—611no—
121#400—612no—
122#399—612no—
123#389—612no—
124#386—612no—
125#385—612no—
126#380—612no—
127#380—611no—
128C61#248711yescharacteristic, complemented, Sylow
129C22×D4C2×D6111yescharacteristic
130C23×C4—612no—
131C23×C4C2×D6111yescharacteristic
132C23×C4C2×D6111yescharacteristic
133C4×D4—24no—
134C2×C4⋊C4—612no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4—612no—
137C2×C4⋊C4—614no—
138C2×C4⋊C4—1224no—
139C2×C4⋊C4C2×D6111yescharacteristic
140C2×C22⋊C4—612no—
141C2×C22⋊C4—614no—
142C2×C22⋊C4C2×D6111yescharacteristic
143C2×C22⋊C4C2×D6111yescharacteristic
144C2×C42C2×D6111yescharacteristic
145#95—614no—
146#95—612no—
147#95—614no—
148C24C22×D6111yescharacteristic
149C24C22×D6111yescharacteristic
150C2×D4—22no—
151C2×D4—22no—
152C2×D4Dic12214yes—
153C22×C4—24no—
154C22×C4—24no—
155C22×C4—22no—
156C22×C4—614no—
157C22×C4—614no—
158C22×C4—1224no—
159C22×C4—2444no—
160C22×C4C22⋊D6114yes—
161C22×C4C22×D6111yescharacteristic
162C22×C4C22×D6111yescharacteristic
163C22×C4C22×D6111yescharacteristic
164C22×C4C22×D6111yescharacteristic
165C22×C4C22×D6111yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—1224no—
168C4⋊C4—1224no—
169C4⋊C4—1224no—
170C4⋊C4—2444no—
171C22⋊C4—22no—
172C22⋊C4—22no—
173C22⋊C4—1224no—
174C22⋊C4—2444no—
175C42—22no—
176C23—22no—
177C23—22no—
178C23—21no—
179C23—22no—
180C23—21no—
181C23—22no—
182C23C2×Dic12212yes—
183C23C2×Dic12212yes—
184C23#1175822212yes—
185C23C2×C22⋊D6112yes—
186C23C23×D6111yescharacteristic
187D4—28no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—28no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—44no—
197C2×C4—1224no—
198C2×C4—1224no—
199C2×C4—1224no—
200C2×C4—1224no—
201C2×C4—1224no—
202C2×C4—1224no—
203C2×C4—2448no—
204C2×C4C2×Dic12212yes—
205C2×C4#1175822414yes—
206C2×C4C2×C22⋊D6112yes—
207C2×C4C2×C22⋊D6112yes—
208C22—24no—
209C22—24no—
210C22—22no—
211C22—22no—
212C22—24no—
213C22—22no—
214C22—42no—
215C22—41no—
216C22—41no—
217C22#1451975614yes—
218C22C22×C22⋊D6111yescharacteristic
219C22C22×Dic12211yescharacteristic
220C22C2×#1175822412yes—
221C22C2×#1175822211yescharacteristic
222C22#1451982312yes—
223C4—22no—
224C4—22no—
225C4—41no—
226C4—41no—
227C4—2444no—
228C4—2444no—
229C4#1451975814yes—
230C2—24no—
231C2—42no—
232C2C2×#1451975611yescharacteristic
233C2C2×#1451975811yescharacteristic
234C2#1684032611yescharacteristic
235C2#1684045812yes—
236C2#1684046912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4×D4×C61C2
hypercenterC2×C4×D4D61
hypocenterC61#2487
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C4⋊Dic61C2semidirect
2. #16839701C2semidirect
3. #16839698C2semidirect
4. #16839660C2semidirect
6. #16839634C2semidirect
7. #16839622C2semidirect
8. #16839622C2semidirect
128. C61#2487semidirect